Therefore rings and Z-algebras are equivalent concepts, in the same way that abelian groups and Z-modules are equivalent.

The Confucian idea of " Rid of the two ends, take the middle " is a Chinese equivalent of Hegel's idea of " thesis, antithesis, and synthesis ", which is a way of reconciling opposites, arriving at some middle ground combining the best of both.

An equivalent way to view an extractor is as a bivariate function

Since ortho derivatives of benzene were never actually found in more than one isomeric form, Kekulé modified his proposal in 1872 and suggested that the benzene molecule oscillates between two equivalent structures, in such a way that the single and double bonds continually interchange positions .< ref >

A MIDI file is in no way a recording of actual music, it is a spreadsheet-like set of instructions, and can use a thousand times less disk space than the equivalent recorded audio.

Flipping front / back and left / right is equivalent to a rotation of 180 degrees about the vertical axis ( in the same way that text which is back-to-front and upside-down simply looks like it has been rotated 180 degrees on the page ).

Enrico Fermi, who developed the theory of beta decay, coined the term neutrino ( the Italian equivalent of " little neutral one ") in 1933 as a way to resolve the confusion.

It is not in any sense a judgement ... hence it is not in any way binding on any state ", while Charles de Visscher argued that in certain situations, an advisory opinion could be binding on the League of Nations Council and, under certain circumstances, some states ; M. Politis agreed, saying that the Court's advisory opinions were equivalent to a binding judgment.

Carl Christian Rafn, in the first detailed study of the Norse exploration of the New World, " Antiquitates Americanae " ( 1837 ), interpreted these times as equivalent to 7. 30am and 4. 30pm, which would put the base a long way south of Newfoundland.

Thus there is no simple way to find an equivalent in the proleptic Julian calendar of a date quoted using the Roman pre-Julian calendar ( AUC or by reference to consuls ).

The idea behind this GA evolution proposed by Emanuel Falkenauer is that solving some complex problems, a. k. a. clustering or partitioning problems where a set of items must be split into disjoint group of items in an optimal way, would better be achieved by making characteristics of the groups of items equivalent to genes.

An 8-bit LRC such as this is equivalent to a cyclic redundancy check using the polynomial x < sup > 8 </ sup >+ 1, but the independence of the bit streams is less clear when looked at that way.

( This is equivalent to the way that an electronic time-domain reflectometer measures reflections caused by changes in the impedance of the cable under test.

In Northern Ireland, the equivalent to a Circuit Judge is a County Court Judge, and they are addressed and titled the same way as a Circuit Judge is in England and Wales.

An equivalent sentence would be " Newly formed bland ideas are inexpressible in an infuriating way.

An equivalent way to express the same process:

An equivalent way to express the same process:

In this way, the polling model is quickly inverted to become equivalent to the callback model, with the application performing its own event dispatching in the original manner.

Because of this correspondence, digital signatures are often described as based on public-key cryptosystems, where signing is equivalent to decryption and verification is equivalent to encryption, but this is not the only way digital signatures are computed.

Walt Disney had long wanted to make a film based on the Uncle Remus storybook, but it wasn't until the mid-1940s that he had found a way to give the stories an adequate film equivalent, in scope and fidelity.

( An equivalent way of stating this is: the smallest back rank interval containing the king, the castling rook, and their destination squares, contains no pieces other than the king and castling rook.

An equivalent way of looking at satisficing is epsilon-optimization ( that means you choose your actions so that the payoff is within epsilon of the optimum ).

There are other equivalent ways of expressing the definition of maximal one-sided and maximal two-sided ideals.

The claim that two formulas are logically equivalent is a statement in the metalanguage, expressing a relationship between two statements p and q.

By ℚ-linearizing the above objects, another way of expressing the above is to say that Artin motives are equivalent to

(" Hey " ( Japanese: へぇ ; Hē ) is the Japanese interjection for expressing genuine surprise, equivalent to a mix of the English interjections " For real?

The federal trial court for the Southern District of New York, though expressing some doubt over the constitutionality of § 4952, declined to invalidate it and awarded a $ 610 judgment to Sarony ( the equivalent of just over $ 12, 000 in 2005 ).

As a unit expressing area, one gō is equivalent to a tenth of a bu or tsubo.

As a unit expressing volume, one gō is equivalent to a tenth of a shō.

The Metabolic Equivalent of Task ( MET ), or simply metabolic equivalent, is a physiological measure expressing the energy cost of physical activities and is defined as the ratio of metabolic rate ( and therefore the rate of energy consumption ) during a specific physical activity to a reference metabolic rate, set by convention to 3. 5 ml O < sub > 2 </ sup >· kg < sup >− 1 </ sup >· min < sup >− 1 </ sup > or equivalently:

He mentions the beats only once '', when he refers to their having revived through mere power and abandonment and the unwillingness to, commit death in life some idea of a decent equivalent between verbal expression and actual experience,, but the entire narrative, is written in the tiresome vocabulary `` of '' that lost `` and '' dying cause, `` and in the '' `` sprung syntax that is supposed to supplant, our mother, tongue.

In the event the total of rupees accruing to the Government of the United States of America as a consequence of sales made pursuant to this Agreement is different from the rupee equivalent of $1,276 million, the amounts available for the purposes specified in paragraph 1, Article 2, will be adjusted proportionately.

In these readings, the double bass is either kept discreetly in the background, or it is dressed in clown's attire -- the musical equivalent of a bull in a china shop.

The cross-sectional area of the cylinders is determined and then the volume of the individual cylinders is computed by multiplying the area by the stroke length, which is the equivalent of the length of the cylinders.

It is well to bear in mind that gasoline will cost from $.80 to $.90 for the equivalent of a United States gallon and while you might prefer a familiar Ford, Chevrolet or even a Cadillac, which are available in some countries, it is probably wiser to choose the smaller European makes which average thirty, thirty-five and even forty miles to the gallon.

For example, when the film is only four minutes old, Neitzbohr refers to a small, Victorian piano stool as `` Wilhelmina '', and we are thereupon subjected to a flashback that informs us that this very piano stool was once used by an epileptic governess whose name, of course, was Doris ( the English equivalent, when passed through middle-Gaelic derivations, of Wilhelmina ).

It is convenient to classify a child's onset ages and completion ages as `` advanced '', `` moderate '' ( modal ), or `` delayed '' according to whether the child's age equivalent `` dots '' appeared to the left of, upon, or to the right of the appropriate short transverse line.

when it represents only itself and on which is its complement ( so that go on is semantically equivalent to board ), on has stronger stress than go does.

When I have instructions to leave is equivalent in meaning to I have instructions that I am to leave this place, dominant stress is ordinarily on leave.

When the same sequence is equivalent in meaning to I have instructions which I am to leave, dominant stress is ordinarily on instructions.

In the first of these sentences if by is the complement of come and Tuesday is an adjunct of time equivalent to on Tuesday, there will be strong stress on by in the spoken language ; ;

In the second sentence if drinking water is a gerundial clause and without drinking water is roughly equivalent in meaning to unless I drink water, there will be stronger stress on water than on drinking ; ;

but if drinking is a gerundial noun modifying water and without drinking water is equivalent to without water for drinking, there will be stronger stress on drinking than on water.

In the Steiners have busy lives without visiting relatives only context can indicate whether visiting relatives is equivalent in meaning to paying visits to relatives or to relatives who are visiting them, and in I looked up the number and I looked up the chimney only the meanings of number and chimney make it clear that up is syntactically a second complement in the first sentence and a preposition followed by its object in the second.